Let \(f:\{1,3,4\}→\{1,2,5\}\) and g:{1,2,5}→{1,3} be given by f = {(1,2),(3,5),(4,1)} and g ={(1,3),(2,3),(5,1)}.Write down gof.
Let \(f:\{1,3,4\}→\{1,2,5\}\) and g:{1,2,5}→{1,3} be given by f = {(1,2),(3,5),(4,1)} and g ={(1,3),(2,3),(5,1)}.Write down gof.
Solution and Explanation
The functions f: {1, 3, 4} → {1, 2, 5} and g: {1, 2, 5} → {1, 3} are defined as f = {(1, 2), (3, 5), (4, 1)} and g = {(1, 3), (2, 3), (5, 1)}.
gof(1)=g(f(1))=g(2)=3 [f (1)=2 and g(2)=3]
gof(3)=g(f(3))=g(5)=1 [f (3)=5 and g(5)=1]
gof(4)=g(f(4))=g(1)=3 [f (4)=1 and g(1)=3]
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R = {(a, b): a ≤ b2 } is neither reflexive nor symmetric nor transitive.Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} as
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Determine whether each of the following relations are reflexive, symmetric, and transitive.
- Relation R in the set A={1,2,3,...13,14} defined as R={(x,y): 3x-y=0}.
- Relation R in the set of N natural numbers defined as R={(x,y): y=x+5 and x<4}.
- Relation R in the set A={1,2,3,4,5,6} defined as R={(x,y): y is divisible by x}.
- Relation R in the set of Z integers defined as R={(x,y): x-y is an integer}
- Relation R in the set of human beings in a town at a particular time given by
- R={(x,y): x and y work at same place}
- R={(x,y): x and y live in the same locality}
- R={(x,y): x is exactly 7 am taller that y}
- R={(x,y): x is wife of y}
- R={(x,y):x is father of y}
Show that the relation R in the set R of real numbers, defined as
R = {(a, b): a ≤ b2 } is neither reflexive nor symmetric nor transitive.Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} as
R = {(a, b): b = a + 1} is reflexive, symmetric or transitive.Show that the relation R in R defined as R = {(a, b): a ≤ b}, is reflexive and transitive
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